[ekiru]

Aren't you assuming (probably incorrectly) that all hardcore gamers rated Competition more highly than all core/casual gamers?

I'm not sure how much less weird allowing for that makes things, but your reasoning for concluding that hardcore gamers with lower Competition scores than the hardcore average make up only 4% of the sample isn't valid.

For example, if half of the hardcore gamers (around 10.5% of the sample) are above the hardcore average and half below, that would put about 81% of the nonhardcore gamers (about 63.5% of the full sample) below the hardcore average and the rest above (about 19% of the full sample).